Why is texture painted model different from rendered version?
Add more lights to the scene.  More light will enable a fairer comparison and give you more control.

Switch to camera view to have a fairer comparison of position.

Pressing Numpad-0 repeatedly will show Camera View and User View.

Use smooth shading.

In the User Preferences Window > System Tab .. there are 3 Solid OpenGL Lights which can affect your viewing.  I am not suggesting you change these settings.  Just know they exist.